In projective geometry, Plücker coordinates[?] refer to a set of homogeneous coordinates introduced initially to embed the set of lines in three dimensions as a quadric in five dimensions. The construction uses 2x2 minor determinants, or equivalently the second exterior power of the underlying vector space of dimension 4. Their study was called line geometry in the nineteenth century. It is now part of the theory of Grassmannians, to which these coordinates apply in generality (kdimensional subspaces of ndimensional space).
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